Arrays

Overview

Teaching: 15 min
Exercises: 5 min

Questions

• How can I access subsets of data?

Objectives

• Select individual values and subsections from data.

Array indexing

Let’s create an 8-by-8 “magic” Matrix:

>> M = magic(8)

ans =

   64    2    3   61   60    6    7   57
    9   55   54   12   13   51   50   16
   17   47   46   20   21   43   42   24
   40   26   27   37   36   30   31   33
   32   34   35   29   28   38   39   25
   41   23   22   44   45   19   18   48
   49   15   14   52   53   11   10   56
    8   58   59    5    4   62   63    1

We want to access a single value from the matrix:

To do that, we must provide its index in parentheses:

>> M(5, 6)

ans = 38

Indices are provided as (row, column). So the index (5, 6) selects the element on the fifth row and sixth column.

An index like (5, 6) selects a single element of an array, but we can also access sections of the matrix, or slices. To access a row of values:

we can do:

>> M(5, :)

ans =

   32   34   35   29   28   38   39   25

Providing : as the index for a dimension selects all elements along that dimension. So, the index (5, :) selects the elements on row 5, and all columns—effectively, the entire row. We can also select multiple rows,

>> M(1:4, :)

ans =

   64    2    3   61   60    6    7   57
    9   55   54   12   13   51   50   16
   17   47   46   20   21   43   42   24
   40   26   27   37   36   30   31   33

and columns:

>> M(:, 6:end)

ans =

    6    7   57
   51   50   16
   43   42   24
   30   31   33
   38   39   25
   19   18   48
   11   10   56
   62   63    1

To select a submatrix,

we have to take slices in both dimensions:

>> M(4:6, 5:7)

ans =

   36   30   31
   28   38   39
   45   19   18

We don’t have to take all the values in the slice—if we provide a stride. Let’s say we want to start with row 2, and subsequently select every third row:

>> M(2:3:end, :)

ans =

    9   55   54   12   13   51   50   16
   32   34   35   29   28   38   39   25
    8   58   59    5    4   62   63    1

And we can also select values in a “checkerboard”,

by taking appropriate strides in both dimensions:

>> M(1:3:end, 2:2:end)

ans =

    2   61    6   57
   26   37   30   33
   15   52   11   56

Slicing

A subsection of an array is called a slice. We can take slices of character strings as well:

>> element = 'oxygen';
>> disp(['first three characters: ', element(1:3)])
>> disp(['last three characters: ', element(4:6)])

first three characters: oxy
last three characters: gen

1. What is the value of element(4:end)? What about element(1:2:end)? Or element(2:end - 1)?

2. For any size array, MATLAB allows us to index with a single colon operator (:). This can have surprising effects. For instance, compare element with element(:). What is size(element) versus size(element(:))? Finally, try using the single colon on the matrix M above: M(:). What seems to be happening when we use the single colon operator for slicing?

Solution

1. Exercises using slicing

    element(4:end)   % Select all elements from 4th to last
    ans =
        'gen'
    element(1:2:end) % Select every other element starting at first
    ans =
        'oye
    element(2:end-1) % Select elements starting with 2nd, until last-but-one
    ans =
        'xyge'
   

2. The colon operator ‘flattens’ a vector or matrix into a column vector. The order of the elements in the resulting vector comes from appending each column of the original array in turn. Have a look at the order of the values in M(:) vs M

Key Points

• M(row, column) indices are used to select data points

• : is used to take slices of data